Senator Brandis said he became quite emotional when the bill passed and the public galleries erupted with cheers and singing.

"To see the galleries of the House of Representatives just explode spontaneously was unforgettable," Senator Brandis told AM.

He said he had celebrated with his Labor counterpart Penny Wong last night.

"I saw Senator Wong at an event and we did have a drink, which doesn't happen very often, but it was a completely non-partisan achievement. This is not owned by the Liberal Party or the Labor Party or any political party. It is owned by the Australian people," Senator Brandis said.

"The Parliament effectively spoke with one voice to give effect to their wishes."